Stochastic variational learning in recurrent spiking networks

Beyond spiking networks: The computational advantages of dendritic amplification and input segregation

The brain can efficiently learn a wide range of tasks, motivating the search for biologically inspired learning rules for improving current artificial intelligence technology. Most biological models are composed of point neurons and cannot achieve state-of-the-art performance in machine learning. Recent works have proposed that input segregation (neurons receive sensory information and higher-order feedback in segregated compartments), and nonlinear dendritic computation would support error backpropagation in biological neurons. However, these approaches require propagating errors with a fine spatiotemporal structure to all the neurons, which is unlikely to be feasible in a biological network. To relax this assumption, we suggest that bursts and dendritic input segregation provide a natural support for target-based learning, which propagates targets rather than errors. A coincidence mechanism between the basal and the apical compartments allows for generating high-frequency bursts of spikes. This architecture supports a burst-dependent learning rule, based on the comparison between the target bursting activity triggered by the teaching signal and the one caused by the recurrent connections, providing support for target-based learning. We show that this framework can be used to efficiently solve spatiotemporal tasks, such as context-dependent store and recall of three-dimensional trajectories, and navigation tasks. Finally, we suggest that this neuronal architecture naturally allows for orchestrating "hierarchical imitation learning", enabling the decomposition of challenging long-horizon decision-making tasks into simpler subtasks. We show a possible implementation of this in a two-level network, where the high network produces the contextual signal for the low network.

Experimental validation of the free-energy principle with in vitro neural networks

Empirical applications of the free-energy principle are not straightforward because they entail a commitment to a particular process theory, especially at the cellular and synaptic levels. Using a recently established reverse engineering technique, we confirm the quantitative predictions of the free-energy principle using in vitro networks of rat cortical neurons that perform causal inference. Upon receiving electrical stimuli-generated by mixing two hidden sources-neurons self-organised to selectively encode the two sources. Pharmacological up- and downregulation of network excitability disrupted the ensuing inference, consistent with changes in prior beliefs about hidden sources. As predicted, changes in effective synaptic connectivity reduced variational free energy, where the connection strengths encoded parameters of the generative model. In short, we show that variational free energy minimisation can quantitatively predict the self-organisation of neuronal networks, in terms of their responses and plasticity. These results demonstrate the applicability of the free-energy principle to in vitro neural networks and establish its predictive validity in this setting.

The Heidelberg Spiking Data Sets for the Systematic Evaluation of Spiking Neural Networks

Spiking neural networks are the basis of versatile and power-efficient information processing in the brain. Although we currently lack a detailed understanding of how these networks compute, recently developed optimization techniques allow us to instantiate increasingly complex functional spiking neural networks in-silico. These methods hold the promise to build more efficient non-von-Neumann computing hardware and will offer new vistas in the quest of unraveling brain circuit function. To accelerate the development of such methods, objective ways to compare their performance are indispensable. Presently, however, there are no widely accepted means for comparing the computational performance of spiking neural networks. To address this issue, we introduce two spike-based classification data sets, broadly applicable to benchmark both software and neuromorphic hardware implementations of spiking neural networks. To accomplish this, we developed a general audio-to-spiking conversion procedure inspired by neurophysiology. Furthermore, we applied this conversion to an existing and a novel speech data set. The latter is the free, high-fidelity, and word-level aligned Heidelberg digit data set that we created specifically for this study. By training a range of conventional and spiking classifiers, we show that leveraging spike timing information within these data sets is essential for good classification accuracy. These results serve as the first reference for future performance comparisons of spiking neural networks.

Error-based or target-based? A unified framework for learning in recurrent spiking networks

The field of recurrent neural networks is over-populated by a variety of proposed learning rules and protocols. The scope of this work is to define a generalized framework, to move a step forward towards the unification of this fragmented scenario. In the field of supervised learning, two opposite approaches stand out, error-based and target-based. This duality gave rise to a scientific debate on which learning framework is the most likely to be implemented in biological networks of neurons. Moreover, the existence of spikes raises the question of whether the coding of information is rate-based or spike-based. To face these questions, we proposed a learning model with two main parameters, the rank of the feedback learning matrix R and the tolerance to spike timing τ_⋆. We demonstrate that a low (high) rank R accounts for an error-based (target-based) learning rule, while high (low) tolerance to spike timing promotes rate-based (spike-based) coding. We show that in a store and recall task, high-ranks allow for lower MSE values, while low-ranks enable a faster convergence. Our framework naturally lends itself to Behavioral Cloning and allows for efficiently solving relevant closed-loop tasks, investigating what parameters (R,τ⋆) are optimal to solve a specific task. We found that a high R is essential for tasks that require retaining memory for a long time (Button and Food). On the other hand, this is not relevant for a motor task (the 2D Bipedal Walker). In this case, we find that precise spike-based coding enables optimal performances. Finally, we show that our theoretical formulation allows for defining protocols to estimate the rank of the feedback error in biological networks. We release a PyTorch implementation of our model supporting GPU parallelization.

Learning in biological or artificial networks means changing the laws governing the network dynamics in order to better behave in a specific situation. However, there exists no consensus on what rules regulate learning in biological systems. To face these questions, we propose a novel theoretical formulation for learning with two main parameters, the number of learning constraints (R) and the tolerance to spike timing (τ_⋆). We demonstrate that a low (high) rank R accounts for an error-based (target-based) learning rule, while high (low) tolerance to spike timing τ_⋆ promotes rate-based (spike-based) coding.

Our approach naturally lends itself to Imitation Learning (and Behavioral Cloning in particular) and we apply it to solve relevant closed-loop tasks such as the button-and-food task, and the 2D Bipedal Walker. The button-and-food is a navigation task that requires retaining a long-term memory, and benefits from a high R. On the other hand, the 2D Bipedal Walker is a motor task and benefits from a low τ_⋆.

Finally, we show that our theoretical formulation suggests protocols to deduce the structure of learning feedback in biological networks.

Multisample Online Learning for Probabilistic Spiking Neural Networks

Spiking neural networks (SNNs) capture some of the efficiency of biological brains for inference and learning via the dynamic, online, and event-driven processing of binary time series. Most existing learning algorithms for SNNs are based on deterministic neuronal models, such as leaky integrate-and-fire, and rely on heuristic approximations of backpropagation through time that enforces constraints such as locality. In contrast, probabilistic SNN models can be trained directly via principled online, local, and update rules that have proven to be particularly effective for resource-constrained systems. This article investigates another advantage of probabilistic SNNs, namely, their capacity to generate independent outputs when queried over the same input. It is shown that the multiple generated output samples can be used during inference to robustify decisions and to quantify uncertainty-a feature that deterministic SNN models cannot provide. Furthermore, they can be leveraged for training in order to obtain more accurate statistical estimates of the log-loss training criterion and its gradient. Specifically, this article introduces an online learning rule based on generalized expectation-maximization (GEM) that follows a three-factor form with global learning signals and is referred to as GEM-SNN. Experimental results on structured output memorization and classification on a standard neuromorphic dataset demonstrate significant improvements in terms of log-likelihood, accuracy, and calibration when increasing the number of samples used for inference and training.

Canonical neural networks perform active inference

This work considers a class of canonical neural networks comprising rate coding models, wherein neural activity and plasticity minimise a common cost function-and plasticity is modulated with a certain delay. We show that such neural networks implicitly perform active inference and learning to minimise the risk associated with future outcomes. Mathematical analyses demonstrate that this biological optimisation can be cast as maximisation of model evidence, or equivalently minimisation of variational free energy, under the well-known form of a partially observed Markov decision process model. This equivalence indicates that the delayed modulation of Hebbian plasticity-accompanied with adaptation of firing thresholds-is a sufficient neuronal substrate to attain Bayes optimal inference and control. We corroborated this proposition using numerical analyses of maze tasks. This theory offers a universal characterisation of canonical neural networks in terms of Bayesian belief updating and provides insight into the neuronal mechanisms underlying planning and adaptive behavioural control.

Brain-inspired global-local learning incorporated with neuromorphic computing

There are two principle approaches for learning in artificial intelligence: error-driven global learning and neuroscience-oriented local learning. Integrating them into one network may provide complementary learning capabilities for versatile learning scenarios. At the same time, neuromorphic computing holds great promise, but still needs plenty of useful algorithms and algorithm-hardware co-designs to fully exploit its advantages. Here, we present a neuromorphic global-local synergic learning model by introducing a brain-inspired meta-learning paradigm and a differentiable spiking model incorporating neuronal dynamics and synaptic plasticity. It can meta-learn local plasticity and receive top-down supervision information for multiscale learning. We demonstrate the advantages of this model in multiple different tasks, including few-shot learning, continual learning, and fault-tolerance learning in neuromorphic vision sensors. It achieves significantly higher performance than single-learning methods. We further implement the model in the Tianjic neuromorphic platform by exploiting algorithm-hardware co-designs and prove that the model can fully utilize neuromorphic many-core architecture to develop hybrid computation paradigm.

Supervised Learning With First-to-Spike Decoding in Multilayer Spiking Neural Networks

Experimental studies support the notion of spike-based neuronal information processing in the brain, with neural circuits exhibiting a wide range of temporally-based coding strategies to rapidly and efficiently represent sensory stimuli. Accordingly, it would be desirable to apply spike-based computation to tackling real-world challenges, and in particular transferring such theory to neuromorphic systems for low-power embedded applications. Motivated by this, we propose a new supervised learning method that can train multilayer spiking neural networks to solve classification problems based on a rapid, first-to-spike decoding strategy. The proposed learning rule supports multiple spikes fired by stochastic hidden neurons, and yet is stable by relying on first-spike responses generated by a deterministic output layer. In addition to this, we also explore several distinct, spike-based encoding strategies in order to form compact representations of presented input data. We demonstrate the classification performance of the learning rule as applied to several benchmark datasets, including MNIST. The learning rule is capable of generalizing from the data, and is successful even when used with constrained network architectures containing few input and hidden layer neurons. Furthermore, we highlight a novel encoding strategy, termed "scanline encoding," that can transform image data into compact spatiotemporal patterns for subsequent network processing. Designing constrained, but optimized, network structures and performing input dimensionality reduction has strong implications for neuromorphic applications.

Target spike patterns enable efficient and biologically plausible learning for complex temporal tasks

Recurrent spiking neural networks (RSNN) in the brain learn to perform a wide range of perceptual, cognitive and motor tasks very efficiently in terms of energy consumption and their training requires very few examples. This motivates the search for biologically inspired learning rules for RSNNs, aiming to improve our understanding of brain computation and the efficiency of artificial intelligence. Several spiking models and learning rules have been proposed, but it remains a challenge to design RSNNs whose learning relies on biologically plausible mechanisms and are capable of solving complex temporal tasks. In this paper, we derive a learning rule, local to the synapse, from a simple mathematical principle, the maximization of the likelihood for the network to solve a specific task. We propose a novel target-based learning scheme in which the learning rule derived from likelihood maximization is used to mimic a specific spatio-temporal spike pattern that encodes the solution to complex temporal tasks. This method makes the learning extremely rapid and precise, outperforming state of the art algorithms for RSNNs. While error-based approaches, (e.g. e-prop) trial after trial optimize the internal sequence of spikes in order to progressively minimize the MSE we assume that a signal randomly projected from an external origin (e.g. from other brain areas) directly defines the target sequence. This facilitates the learning procedure since the network is trained from the beginning to reproduce the desired internal sequence. We propose two versions of our learning rule: spike-dependent and voltage-dependent. We find that the latter provides remarkable benefits in terms of learning speed and robustness to noise. We demonstrate the capacity of our model to tackle several problems like learning multidimensional trajectories and solving the classical temporal XOR benchmark. Finally, we show that an online approximation of the gradient ascent, in addition to guaranteeing complete locality in time and space, allows learning after very few presentations of the target output. Our model can be applied to different types of biological neurons. The analytically derived plasticity learning rule is specific to each neuron model and can produce a theoretical prediction for experimental validation.

Poisson balanced spiking networks

An important problem in computational neuroscience is to understand how networks of spiking neurons can carry out various computations underlying behavior. Balanced spiking networks (BSNs) provide a powerful framework for implementing arbitrary linear dynamical systems in networks of integrate-and-fire neurons. However, the classic BSN model requires near-instantaneous transmission of spikes between neurons, which is biologically implausible. Introducing realistic synaptic delays leads to an pathological regime known as "ping-ponging", in which different populations spike maximally in alternating time bins, causing network output to overshoot the target solution. Here we document this phenomenon and provide a novel solution: we show that a network can have realistic synaptic delays while maintaining accuracy and stability if neurons are endowed with conditionally Poisson firing. Formally, we propose two alternate formulations of Poisson balanced spiking networks: (1) a "local" framework, which replaces the hard integrate-and-fire spiking rule within each neuron by a "soft" threshold function, such that firing probability grows as a smooth nonlinear function of membrane potential; and (2) a "population" framework, which reformulates the BSN objective function in terms of expected spike counts over the entire population. We show that both approaches offer improved robustness, allowing for accurate implementation of network dynamics with realistic synaptic delays between neurons. Both Poisson frameworks preserve the coding accuracy and robustness to neuron loss of the original model and, moreover, produce positive correlations between similarly tuned neurons, a feature of real neural populations that is not found in the deterministic BSN. This work unifies balanced spiking networks with Poisson generalized linear models and suggests several promising avenues for future research.

Low-dimensional dynamics for working memory and time encoding

Our decisions often depend on multiple sensory experiences separated by time delays. The brain can remember these experiences and, simultaneously, estimate the timing between events. To understand the mechanisms underlying working memory and time encoding, we analyze neural activity recorded during delays in four experiments on nonhuman primates. To disambiguate potential mechanisms, we propose two analyses, namely, decoding the passage of time from neural data and computing the cumulative dimensionality of the neural trajectory over time. Time can be decoded with high precision in tasks where timing information is relevant and with lower precision when irrelevant for performing the task. Neural trajectories are always observed to be low-dimensional. In addition, our results further constrain the mechanisms underlying time encoding as we find that the linear "ramping" component of each neuron's firing rate strongly contributes to the slow timescale variations that make decoding time possible. These constraints rule out working memory models that rely on constant, sustained activity and neural networks with high-dimensional trajectories, like reservoir networks. Instead, recurrent networks trained with backpropagation capture the time-encoding properties and the dimensionality observed in the data.

An Attempt at a Unified Theory of the Neocortical Microcircuit in Sensory Cortex

The neocortex performs a wide range of functions, including working memory, sensory perception, and motor planning. Despite this diversity in function, evidence suggests that the neocortex is made up of repeating subunits ("macrocolumns"), each of which is largely identical in circuitry. As such, the specific computations performed by these macrocolumns are of great interest to neuroscientists and AI researchers. Leading theories of this microcircuit include models of predictive coding, hierarchical temporal memory (HTM), and Adaptive Resonance Theory (ART). However, these models have not yet explained: (1) how microcircuits learn sequences input with delay (i.e., working memory); (2) how networks of columns coordinate processing on precise timescales; or (3) how top-down attention modulates sensory processing. I provide a theory of the neocortical microcircuit that extends prior models in all three ways. Additionally, this theory provides a novel working memory circuit that extends prior models to support simultaneous multi-item storage without disrupting ongoing sensory processing. I then use this theory to explain the functional origin of a diverse set of experimental findings, such as cortical oscillations.

Discrete Langevin machine: Bridging the gap between thermodynamic and neuromorphic systems

A formulation of Langevin dynamics for discrete systems is derived as a class of generic stochastic processes. The dynamics simplify for a two-state system and suggest a network architecture which is implemented by the Langevin machine. The Langevin machine represents a promising approach to compute successfully quantitative exact results of Boltzmann distributed systems by LIF neurons. Besides a detailed introduction of the dynamics, different simplified models of a neuromorphic hardware system are studied with respect to a control of emerging sources of errors.

Multi-context blind source separation by error-gated Hebbian rule

Animals need to adjust their inferences according to the context they are in. This is required for the multi-context blind source separation (BSS) task, where an agent needs to infer hidden sources from their context-dependent mixtures. The agent is expected to invert this mixing process for all contexts. Here, we show that a neural network that implements the error-gated Hebbian rule (EGHR) with sufficiently redundant sensory inputs can successfully learn this task. After training, the network can perform the multi-context BSS without further updating synapses, by retaining memories of all experienced contexts. This demonstrates an attractive use of the EGHR for dimensionality reduction by extracting low-dimensional sources across contexts. Finally, if there is a common feature shared across contexts, the EGHR can extract it and generalize the task to even inexperienced contexts. The results highlight the utility of the EGHR as a model for perceptual adaptation in animals.

Dopaminergic Modulation of Synaptic Plasticity, Its Role in Neuropsychiatric Disorders, and Its Computational Modeling

Neuromodulators modify intrinsic characteristics of the nervous system in order to reconfigure the functional properties of neural circuits. This reconfiguration is crucial for the flexibility of the nervous system to respond on an input-modulated basis. Such a functional rearrangement is realized by modification of intrinsic properties of the neural circuits including synaptic interactions. Dopamine is an important neuromodulator involved in motivation and stimulus-reward learning process, and adjusts synaptic dynamics in multiple time scales through different pathways. The modification of synaptic plasticity by dopamine underlies the change in synaptic transmission and integration mechanisms, which affects intrinsic properties of the neural system including membrane excitability, probability of neurotransmitters release, receptors’ response to neurotransmitters, protein trafficking, and gene transcription. Dopamine also plays a central role in behavioral control, whereas its malfunction can cause cognitive disorders. Impaired dopamine signaling is implicated in several neuropsychiatric disorders such as Parkinson’s disease, drug addiction, schizophrenia, attention-deficit/hyperactivity disorder, obsessive-compulsive disorder and Tourette’s syndrome. Therefore, dopamine plays a crucial role in the nervous system, where its proper modulation of neural circuits may enhance plasticity-related procedures, but disturbances in dopamine signaling might be involved in numerous neuropsychiatric disorders. In recent years, several computational models are proposed to formulate the involvement of dopamine in synaptic plasticity or neuropsychiatric disorders and address their connection based on the experimental findings.

Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of NeoHebbian Three-Factor Learning Rules

Most elementary behaviors such as moving the arm to grasp an object or walking into the next room to explore a museum evolve on the time scale of seconds; in contrast, neuronal action potentials occur on the time scale of a few milliseconds. Learning rules of the brain must therefore bridge the gap between these two different time scales. Modern theories of synaptic plasticity have postulated that the co-activation of pre- and postsynaptic neurons sets a flag at the synapse, called an eligibility trace, that leads to a weight change only if an additional factor is present while the flag is set. This third factor, signaling reward, punishment, surprise, or novelty, could be implemented by the phasic activity of neuromodulators or specific neuronal inputs signaling special events. While the theoretical framework has been developed over the last decades, experimental evidence in support of eligibility traces on the time scale of seconds has been collected only during the last few years. Here we review, in the context of three-factor rules of synaptic plasticity, four key experiments that support the role of synaptic eligibility traces in combination with a third factor as a biological implementation of neoHebbian three-factor learning rules.

SuperSpike: Supervised Learning in Multilayer Spiking Neural Networks

A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in silico. Here we revisit the problem of supervised learning in temporally coding multilayer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three-factor learning rule capable of training multilayer networks of deterministic integrate-and-fire neurons to perform nonlinear computations on spatiotemporal spike patterns. Second, inspired by recent results on feedback alignment, we compare the performance of our learning rule under different credit assignment strategies for propagating output errors to hidden units. Specifically, we test uniform, symmetric, and random feedback, finding that simpler tasks can be solved with any type of feedback, while more complex tasks require symmetric feedback. In summary, our results open the door to obtaining a better scientific understanding of learning and computation in spiking neural networks by advancing our ability to train them to solve nonlinear problems involving transformations between different spatiotemporal spike time patterns.

Conduction Delay Learning Model for Unsupervised and Supervised Classification of Spatio-Temporal Spike Patterns

Precise spike timing is considered to play a fundamental role in communications and signal processing in biological neural networks. Understanding the mechanism of spike timing adjustment would deepen our understanding of biological systems and enable advanced engineering applications such as efficient computational architectures. However, the biological mechanisms that adjust and maintain spike timing remain unclear. Existing algorithms adopt a supervised approach, which adjusts the axonal conduction delay and synaptic efficacy until the spike timings approximate the desired timings. This study proposes a spike timing-dependent learning model that adjusts the axonal conduction delay and synaptic efficacy in both unsupervised and supervised manners. The proposed learning algorithm approximates the Expectation-Maximization algorithm, and classifies the input data encoded into spatio-temporal spike patterns. Even in the supervised classification, the algorithm requires no external spikes indicating the desired spike timings unlike existing algorithms. Furthermore, because the algorithm is consistent with biological models and hypotheses found in existing biological studies, it could capture the mechanism underlying biological delay learning.

Learning with three factors: modulating Hebbian plasticity with errors

Synaptic plasticity is a central theme in neuroscience. A framework of three-factor learning rules provides a powerful abstraction, helping to navigate through the abundance of models of synaptic plasticity. It is well-known that the dopamine modulation of learning is related to reward, but theoretical models predict other functional roles of the modulatory third factor; it may encode errors for supervised learning, summary statistics of the population activity for unsupervised learning or attentional feedback. Specialized structures may be needed in order to generate and propagate third factors in the neural network.

Memory replay in balanced recurrent networks

Complex patterns of neural activity appear during up-states in the neocortex and sharp waves in the hippocampus, including sequences that resemble those during prior behavioral experience. The mechanisms underlying this replay are not well understood. How can small synaptic footprints engraved by experience control large-scale network activity during memory retrieval and consolidation? We hypothesize that sparse and weak synaptic connectivity between Hebbian assemblies are boosted by pre-existing recurrent connectivity within them. To investigate this idea, we connect sequences of assemblies in randomly connected spiking neuronal networks with a balance of excitation and inhibition. Simulations and analytical calculations show that recurrent connections within assemblies allow for a fast amplification of signals that indeed reduces the required number of inter-assembly connections. Replay can be evoked by small sensory-like cues or emerge spontaneously by activity fluctuations. Global-potentially neuromodulatory-alterations of neuronal excitability can switch between network states that favor retrieval and consolidation.

Deep Learning with Dynamic Spiking Neurons and Fixed Feedback Weights

Recent work in computer science has shown the power of deep learning driven by the backpropagation algorithm in networks of artificial neurons. But real neurons in the brain are different from most of these artificial ones in at least three crucial ways: they emit spikes rather than graded outputs, their inputs and outputs are related dynamically rather than by piecewise-smooth functions, and they have no known way to coordinate arrays of synapses in separate forward and feedback pathways so that they change simultaneously and identically, as they do in backpropagation. Given these differences, it is unlikely that current deep learning algorithms can operate in the brain, but we that show these problems can be solved by two simple devices: learning rules can approximate dynamic input-output relations with piecewise-smooth functions, and a variation on the feedback alignment algorithm can train deep networks without having to coordinate forward and feedback synapses. Our results also show that deep spiking networks learn much better if each neuron computes an intracellular teaching signal that reflects that cell's nonlinearity. With this mechanism, networks of spiking neurons show useful learning in synapses at least nine layers upstream from the output cells and perform well compared to other spiking networks in the literature on the MNIST digit recognition task.

Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities.

The question of how the brain self-organizes to develop precisely tuned neurons has puzzled neuroscientists at least since the discoveries of Hubel and Wiesel. In the past decades, a variety of theories and models have been proposed to describe receptive field formation, notably V1 simple cells, from natural inputs. We cut through the jungle of candidate explanations by demonstrating that in fact a single principle is sufficient to explain receptive field development. Our results follow from two major insights. First, we show that many representative models of sensory development are in fact implementing variations of a common principle: nonlinear Hebbian learning. Second, we reveal that nonlinear Hebbian learning is sufficient for receptive field formation through sensory inputs. The surprising result is that our findings are robust of specific details of a model, and allows for robust predictions on the learned receptive fields. Nonlinear Hebbian learning is therefore general in two senses: it applies to many models developed by theoreticians, and to many sensory modalities studied by experimental neuroscientists.

Supervised Learning in Spiking Neural Networks for Precise Temporal Encoding

Precise spike timing as a means to encode information in neural networks is biologically supported, and is advantageous over frequency-based codes by processing input features on a much shorter time-scale. For these reasons, much recent attention has been focused on the development of supervised learning rules for spiking neural networks that utilise a temporal coding scheme. However, despite significant progress in this area, there still lack rules that have a theoretical basis, and yet can be considered biologically relevant. Here we examine the general conditions under which synaptic plasticity most effectively takes place to support the supervised learning of a precise temporal code. As part of our analysis we examine two spike-based learning methods: one of which relies on an instantaneous error signal to modify synaptic weights in a network (INST rule), and the other one relying on a filtered error signal for smoother synaptic weight modifications (FILT rule). We test the accuracy of the solutions provided by each rule with respect to their temporal encoding precision, and then measure the maximum number of input patterns they can learn to memorise using the precise timings of individual spikes as an indication of their storage capacity. Our results demonstrate the high performance of the FILT rule in most cases, underpinned by the rule’s error-filtering mechanism, which is predicted to provide smooth convergence towards a desired solution during learning. We also find the FILT rule to be most efficient at performing input pattern memorisations, and most noticeably when patterns are identified using spikes with sub-millisecond temporal precision. In comparison with existing work, we determine the performance of the FILT rule to be consistent with that of the highly efficient E-learning Chronotron rule, but with the distinct advantage that our FILT rule is also implementable as an online method for increased biological realism.

Neuromodulated Spike-Timing-Dependent Plasticity, and Theory of Three-Factor Learning Rules

Classical Hebbian learning puts the emphasis on joint pre- and postsynaptic activity, but neglects the potential role of neuromodulators. Since neuromodulators convey information about novelty or reward, the influence of neuromodulators on synaptic plasticity is useful not just for action learning in classical conditioning, but also to decide "when" to create new memories in response to a flow of sensory stimuli. In this review, we focus on timing requirements for pre- and postsynaptic activity in conjunction with one or several phasic neuromodulatory signals. While the emphasis of the text is on conceptual models and mathematical theories, we also discuss some experimental evidence for neuromodulation of Spike-Timing-Dependent Plasticity. We highlight the importance of synaptic mechanisms in bridging the temporal gap between sensory stimulation and neuromodulatory signals, and develop a framework for a class of neo-Hebbian three-factor learning rules that depend on presynaptic activity, postsynaptic variables as well as the influence of neuromodulators.

Central Cholinergic Neurons Are Rapidly Recruited by Reinforcement Feedback

Basal forebrain cholinergic neurons constitute a major neuromodulatory system implicated in normal cognition and neurodegenerative dementias. Cholinergic projections densely innervate neocortex, releasing acetylcholine to regulate arousal, attention, and learning. However, their precise behavioral function is poorly understood because identified cholinergic neurons have never been recorded during behavior. To determine which aspects of cognition their activity might support, we recorded cholinergic neurons using optogenetic identification in mice performing an auditory detection task requiring sustained attention. We found that a non-cholinergic basal forebrain population-but not cholinergic neurons-were correlated with trial-to-trial measures of attention. Surprisingly, cholinergic neurons responded to reward and punishment with unusual speed and precision (18 ± 3 ms). Cholinergic responses were scaled by the unexpectedness of reinforcement and were highly similar across neurons and two nuclei innervating distinct cortical areas. These results reveal that the cholinergic system broadcasts a rapid and precisely timed reinforcement signal, supporting fast cortical activation and plasticity.

Synaptic consolidation: from synapses to behavioral modeling

Synaptic plasticity, a key process for memory formation, manifests itself across different time scales ranging from a few seconds for plasticity induction up to hours or even years for consolidation and memory retention. We developed a three-layered model of synaptic consolidation that accounts for data across a large range of experimental conditions. Consolidation occurs in the model through the interaction of the synaptic efficacy with a scaffolding variable by a read-write process mediated by a tagging-related variable. Plasticity-inducing stimuli modify the efficacy, but the state of tag and scaffold can only change if a write protection mechanism is overcome. Our model makes a link from depotentiation protocols in vitro to behavioral results regarding the influence of novelty on inhibitory avoidance memory in rats.

A spiking neural network model of model-free reinforcement learning with high-dimensional sensory input and perceptual ambiguity

A theoretical framework of reinforcement learning plays an important role in understanding action selection in animals. Spiking neural networks provide a theoretically grounded means to test computational hypotheses on neurally plausible algorithms of reinforcement learning through numerical simulation. However, most of these models cannot handle observations which are noisy, or occurred in the past, even though these are inevitable and constraining features of learning in real environments. This class of problem is formally known as partially observable reinforcement learning (PORL) problems. It provides a generalization of reinforcement learning to partially observable domains. In addition, observations in the real world tend to be rich and high-dimensional. In this work, we use a spiking neural network model to approximate the free energy of a restricted Boltzmann machine and apply it to the solution of PORL problems with high-dimensional observations. Our spiking network model solves maze tasks with perceptually ambiguous high-dimensional observations without knowledge of the true environment. An extended model with working memory also solves history-dependent tasks. The way spiking neural networks handle PORL problems may provide a glimpse into the underlying laws of neural information processing which can only be discovered through such a top-down approach.

Racing to learn: statistical inference and learning in a single spiking neuron with adaptive kernels

This paper describes the Synapto-dendritic Kernel Adapting Neuron (SKAN), a simple spiking neuron model that performs statistical inference and unsupervised learning of spatiotemporal spike patterns. SKAN is the first proposed neuron model to investigate the effects of dynamic synapto-dendritic kernels and demonstrate their computational power even at the single neuron scale. The rule-set defining the neuron is simple: there are no complex mathematical operations such as normalization, exponentiation or even multiplication. The functionalities of SKAN emerge from the real-time interaction of simple additive and binary processes. Like a biological neuron, SKAN is robust to signal and parameter noise, and can utilize both in its operations. At the network scale neurons are locked in a race with each other with the fastest neuron to spike effectively "hiding" its learnt pattern from its neighbors. The robustness to noise, high speed, and simple building blocks not only make SKAN an interesting neuron model in computational neuroscience, but also make it ideal for implementation in digital and analog neuromorphic systems which is demonstrated through an implementation in a Field Programmable Gate Array (FPGA). Matlab, Python, and Verilog implementations of SKAN are available at: http://www.uws.edu.au/bioelectronics_neuroscience/bens/reproducible_research.

Ensembles of spiking neurons with noise support optimal probabilistic inference in a dynamically changing environment

It has recently been shown that networks of spiking neurons with noise can emulate simple forms of probabilistic inference through “neural sampling”, i.e., by treating spikes as samples from a probability distribution of network states that is encoded in the network. Deficiencies of the existing model are its reliance on single neurons for sampling from each random variable, and the resulting limitation in representing quickly varying probabilistic information. We show that both deficiencies can be overcome by moving to a biologically more realistic encoding of each salient random variable through the stochastic firing activity of an ensemble of neurons. The resulting model demonstrates that networks of spiking neurons with noise can easily track and carry out basic computational operations on rapidly varying probability distributions, such as the odds of getting rewarded for a specific behavior. We demonstrate the viability of this new approach towards neural coding and computation, which makes use of the inherent parallelism of generic neural circuits, by showing that this model can explain experimentally observed firing activity of cortical neurons for a variety of tasks that require rapid temporal integration of sensory information.

The Markov Chain Monte Carlo (MCMC) approach to probabilistic inference for a distribution is to draw a sequence of samples from and to carry out computational operations via simple online computations on such a sequence. But such a sequential computational process takes time, and therefore this simple version of the MCMC approach runs into problems when one needs to carry out probabilistic inference for rapidly varying distributions. This difficulty also affects all currently existing models for emulating MCMC sampling by networks of stochastically firing neurons. We show here that by moving to a space-rate approach where salient probabilities are encoded through the spiking activity of ensembles of neurons, rather than by single neurons, this problem can be solved. In this way even theoretically optimal models for dealing with time varying distributions through sequential Monte Carlo sampling, so called particle filters, can be emulated by networks of spiking neurons. Each spike of a neuron in an ensemble represents in this approach a “particle” (or vote) for a particular value of a time-varying random variable. In other words, neural circuits can speed up computations based on Monte Carlo sampling through their inherent parallelism.